A new proof of a lemma by Phelps

Antonia E. Cardwell

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-3

Abstract:

We give a different proof of a lemma by Phelps (1960) whichasserts, roughly speaking, that if two norm-one functionals f and g have their hyperplanes f − 1 ( 0 ) and g − 1 ( 0 ) sufficiently close together, then either ‖ f − g ‖ or ‖ f + g ‖ must be small. We also extend this result to a complexBanach space.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:028063

DOI: 10.1155/IJMMS/2006/28063

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